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We investigate the stability of the electroweak Z-string at high temperatures. Our results show that while finite temperature corrections can improve the stability of the Z-string, their effect is not strong enough to stabilize the Z-string in the standard electroweak model. Consequently, the Z-string will be unstable even under the conditions present during the electroweak phase transition. We then consider phenomenologically viable models based on the gauge group $SU(2)_L times SU(2)_R times U(1)_{B-L}$ and show that metastable strings exist and are stable to small perturbations for a large region of the parameter space for these models. We also show that these strings are superconducting with bosonic charge carriers. The string superconductivity may be able to stabilize segments and loops against dynamical contraction. Possible implications of these strings for cosmology are discussed.
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A metastable cosmic-string network is a generic consequence of many grand unified theories (GUTs) when combined with cosmic inflation. Metastable cosmic strings are not topologically stable, but decay on cosmic time scales due to pair production of GUT monopoles. This leads to a network consisting of metastable long strings on superhorizon scales as well as of string loops and segments on subhorizon scales. We compute for the first time the complete stochastic gravitational-wave background (SGWB) arising from all these network constituents, including several technical improvements to both the derivation of the loop and segment contributions. We find that the gravitational waves emitted by string loops provide the main contribution to the gravitational-wave spectrum in the relevant parameter space. The resulting spectrum is consistent with the tentative signal observed by the NANOGrav and Parkes pulsar timing collaborations for a string tension of Gmu ~ 10^-11...-7 and has ample discovery space for ground- and space-based detectors. For GUT-scale string tensions, Gmu ~ 10^-8...-7, metastable strings predict a SGWB in the LIGO-Virgo-KAGRA band that could be discovered in the near future.
We present a successful realization of sneutrino tribrid inflation model based on a gauged $U(1)_{B-L}$ extension of Minimal Supersymmetric Standard Model (MSSM). A single interaction term involving the $B-L$ Higgs field and the right-handed neutrinos serves multiple purposes. These include the generation of heavy Majorana masses for the right-handed neutrinos to provide an explanation for the tiny neutrino masses via the seesaw mechanism, a realistic scenario for reheating and non-thermal leptogenesis with a reheat temperature as low as $10^6$ GeV, and a successful realization of inflation with right-handed sneutrino as the inflaton. The matter parity which helps avoid rapid proton decay survives as a $Z_{2}$ subgroup of a $U(1)$ $R$-symmetry. Depending on the choice of model parameters yields the following predicted range of the tensor to scalar ratio, $3 times 10^{-11}lesssim rlesssim 7times 10^{-4}$ ($ 6 times 10^{-7} lesssim r lesssim 0.01 $), and the running of the scalar spectral index, $-0.00022 lesssim dn_s/dln k lesssim -0.0026$ ($-0.00014 lesssim dn_s/dln k lesssim 0.005$), along with the $B-L$ breaking scale, $ 3 times 10^{14}lesssim M/ text{GeV}lesssim 5 times 10^{15}$ ($ 6 times 10^{15}lesssim M/ text{GeV}lesssim 2 times 10^{16}$), calculated at the central value of the scalar spectral index, $n_s =0.966$, reported by Planck 2018. The possibility of realizing metastable cosmic strings in a grand unified theory setup is briefly discussed. The metastable cosmic string network admits string tension values in the range $10^{-8} lesssim Gmu_s lesssim 10^{-6}$, and predicts a stochastic gravitational wave background lying within the 2-$sigma$ bounds of the recent NANOGrav 12.5-yr data.
We study the realistic structure of F-term Nambu-Goto cosmic strings forming in a general supersymmetric Grand Unified Theory implementation, assuming standard hybrid inflation. Examining the symmetry breaking of the unification gauge group down to the Standard Model, we discuss the minimal field content necessary to describe abelian cosmic strings appearing at the end of inflation. We find that several fields will condense in most theories, questioning the plausible occurrence of associated currents (bosonic and fermionic). We perturbatively evaluate the modification of their energy per unit length due to the condensates. We provide a criterion for comparing the usual abelian Higgs approximation used in cosmology to realistic situations.
We first examine the microstructure of a cosmic string endowed with two simple Abelian currents. This microstructure depends on two state parameters. We then provide the macroscopic description of such a string and show that it depends on an additional Lorentz-invariant state parameter that relates the two currents. We find that in most of the parameter space, the two-current string is essentially equivalent to the single current-carrying string, i.e., only one field condenses onto the defect. In the regions where two currents are present, we find that as far as stability is concerned, one can approximate the dynamics with good accuracy using an analytic model based on either a logarithmic (on the electric side, i.e., for timelike currents) or a rational (on the magnetic side, i.e., for spacelike currents) worldsheet Lagrangian.
We study the bosonic structure of $F$-term Nambu-Goto cosmic strings forming in a realistic SO(10) implementation, assuming standard hybrid inflation. We describe the supersymmetric grand unified theory, and its spontaneous symmetry breaking scheme in parallel with the inflationary process. We also write the explicit tensor formulation of its scalar sector, focusing on the sub-representations singlet under the standard model, which is sufficient to describe the string structure. We then introduce an ansatz for abelian cosmic strings, discussing in details the hypothesis, and write down the field equations and boundary conditions. Finally, after doing a perturbative study of the model, we present and discuss the results obtained with numerical solutions of the string structure.
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